I have a few keywords where my website is high ranking(2nd and 3rd result). For instance, I have 3 blog posts covering a certain kind of modem.

Is it common for search engines to consider a website popular in a "category"? For instance, if I was the first result for "foobar" with one page, and then added another separate page which mentioned "foobar"(and maybe a link from the original page), would a search engine prioritize this separate page when compared to a completely separate website with a page with the same content?

1 Answer
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This happens a lot and is part of a search engines consideration: What kind of industry / sector / line of business, or, as you name it, "category" can a site be correlated?

A strong signal for such an assignement are keywords, links, and more and more social mentions. Tools like from Sistrix compute this similar to give you a hint about your site (or your competitor's).

Example (btw, this is for stackexchange):

What is it good for? If your site is related to a specific industry, say "Sports" and gets lot of links from hairdresser or gardener sites (...) those can be easily devaluated. Links from "matching" sites will pass more link juice.

Every piece of (quality) content you create onsite will support your overall theme.

To answer the last of your questions: In theory it could be prioritized if your content or your site is already considered as an authority on that topic, or if the content outranks the other because it is considered as the unique, older or more trusted source. It the page that "mentions" the other is not that helpful as the other it might not be considered.

Even more: If the search term results in a SERP with universal search elements or local results (maps, videos, images, g+ / authors, product recommendations) it's less likely for your just-mentioning-page to get listed (this is not directly what you asked, just another aspect).

Could you back up your answer with sources, logic, or easily verifiable details? Just making a claim without backing it up is not enough, because then nobody can verify your answer.
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ChristofianNov 9 '12 at 19:50

Can you also give a link for Sistrix compute? I'd be curious to run this on my website, but I can't find it. (the only significant reference to it is this answer in google)
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EarlzNov 10 '12 at 4:05

@Christofian Added some sources. To be fair: "easily verifiable sources" is not always possible in the field of SEO. You have to put together the pieces and observations of your own work and the one of the community. Dig deeper with searching for "context relevancy linkbuilding" - things like that.
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initallNov 10 '12 at 9:36